Interpreting a log transformed multiple regression model in R - r

I am trying to build a model that can predict SalePrice using independent variables that denote various house features. I used Multiple Regression Model, and also found that some predictor variables needed to be transformed, as well as the response variable.
My final model is as follows;
Model Output
How do I interpret this result? Can I conclude that a one unit increase in Years Since Remodel causes a -2.905e-03 change in log of Sale Price? How do I make this interpretation easier to understand? Thank you.

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Changing coefficients in logistic regression

I will try to explain my problem as best as i can. I am trying to externally validate a prediction model, made by one of my colleagues. For the external validation, I have collected data from a set of new patients.
I want to test the accuracy of the prediction model on this new dataset. Online i have found a way to do so, using the coef.orig function to extract de coefficients of the original prediction model (see the picture i added). Here comes the problem, it is impossible for me to repeat the steps my colleague did to obtain the original prediction model. He used multiple imputation and bootstrapping for the development and internal validation, making it very complex to repeat his steps. What I do have, is the computed intercept and coefficients from the original model. Step 1 from the picture i added, could therefor be skipped.
My question is, how can I add these coefficients into the regression model, without the use of the 'coef()' function?
Steps to externally validate the prediction model:
The coefficients I need to use:
I thought that the offset function would possibly be of use, however this does not allow me to set the intercept and all the coefficients for the variables at the same time

How to interpret a VAR model without sigificant coefficients?

I am trying to investigate the relationship between some Google Trends Data and Stock Prices.
I performed the augmented ADF Test and KPSS test to make sure that both time series are integrated of the same order (I(1)).
However, after I took the first differences, the ACF plot was completely insigificant (except for 1 of course), which told me that the differenced series are behaving like white noise.
Nevertheless I tried to estimate a VAR model which you can see attached.
As you can see, only one constant is significant. I have already read that because Stocks.ts.l1 is not significant in the equation for GoogleTrends and GoogleTrends.ts.l1 is not significant in the equation for Stocks, there is no dynamic between the two time series and both can also be models independently from each other with a AR(p) model.
I checked the residuals of the model. They fulfill the assumptions (normally distributed residuals are not totally given but ok, there is homoscedasticity, its stable and there is no autocorrelation).
But what does it mean if no coefficient is significant as in the case of the Stocks.ts equation? Is the model just inappropriate to fit the data, because the data doesn't follow an AR process. Or is the model just so bad, that a constant would describe the data better than the model? Or a combination of the previous questions? Any suggestions how I could proceed my analysis?
Thanks in advance

Ordered Probit R

I'm trying create an ordered probit model in R. My independent variable is categorical, my dependent variable is ordinal. I'm using the polr command and it does go through. When I run the command, I get the log odds for the different variables. I have converted them into odds ratios using the exp command. As far as I understand it, these odds ratios tell me what the probability is of my dependent variable going up one category every time my independent variable "goes up" one category. Is that correct? I'm somewhat confused because in the case of the independent variable, it's not really an increase since they are just categories.
My second question concerns the interpretation of the polr. All I get are the odds ratios. How would you recommend I get additional information on the suitability of the ordered probit? Thanks!

R: Which variables to include in model?

I'm fairly new to R and am currently trying to find the best model to predict my dependent variable from a number of predictor variables. I have 20 precictor variables and I want to see which ones I should include in my model and which ones I should exclude.
I am currently just running models with different predictor variables in each and comparing them to see which one has the lowest AIC, but this is taking a really long time. Is there an easier way to do this?
Thank you in advance.
This is more of a theoretical question actually...
In principle, if all of the predictors are actually exogenous to the model, they can all be included together and assuming you have enough data (N >> 20) and they are not too similar (which could give rise to multi-collinearity), that should help prediction. In practice, you need to think about whether each of (or any of) your predictors are actually exogenous to the model (that is, independent of the error term in the model). If they are not, then they will impart a bias on the estimates. (Also, omitting explanatory variables that are actually necessary imparts a bias.)
If predictive accuracy (even spurious in-sample accuracy) is the goal, then techniques like LASSO (as mentioned in the comments) could also help.

In R, how to add an external variable to an ARIMA model?

Does anyone here know how I can specify additional external variables to an ARIMA model ?
In my case I am trying to make a volatility model and I would like to add the squared returns to model an ARCH.
The reason I am not using GARCH models, is that I am only interested in the volatility forecasts and the GARCH models present their errors on their returns which is not the subject of my study.
I would like to add an external variable and see the R^2 and p-values to see if the coefficient is statistically significant.
I know that this is a very old question but for people like me who were wondering this you need to use cbind with xreg.
For Example:
Arima(X,order=c(3,1,3),xreg = cbind(ts1,ts2,ts3))
Each external time series should be the same length as the original.

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